Methods and systems for autonomous generation of shortest lateral paths for unmanned aerial systems

ABSTRACT

Methods and systems for autonomous generation of shortest lateral paths for unmanned aerial systems are described. An example system includes memory storing code and at least one processor to execute the code to cause the at least one processor to access an initial scenario including a source point, a target point, and a no flight zone, determine a computation time for identifying a lateral path for an aircraft to traverse that avoids the no flight zone, determine whether the determined computation time satisfies a threshold of a reference computation time, change the first number of vertices to a second number of vertices when the reference computation time is not satisfied, determine a buffer area surrounding the no flight zone, construct a visibility graph including lateral paths, and identify one of the lateral paths as being shorter than others of the lateral paths.

RELATED APPLICATION

This patent claims the benefit of U.S. application Ser. No. 15/206,189,filed on Jul. 8, 2016, which claims the benefit of European PatentApplication No. EP15382365.3 filed on Jul. 14, 2015. U.S. applicationSer. No. 15/206,189 and European Patent Application No. EP15382365.3 arehereby incorporated herein by reference in their entireties.

BACKGROUND

Unmanned aircraft may be used to fly between a source point and a targetpoint. No flight zones may be present in some areas.

SUMMARY

An example system includes memory storing computer readable code and atleast one processor to execute the computer readable code to cause theat least one processor to access an initial scenario including a sourcepoint, a target point, and a no flight zone, determine a computationtime for identifying a lateral path for an aircraft to traverse thatavoids the no flight zone, the computation time being associated with afirst number of vertices of the no flight zone, determine whether thedetermined computation time satisfies a threshold of a referencecomputation time, when the computation time does not satisfy thethreshold of the reference computation time, change the first number ofvertices of the no flight zone to a second number of vertices of the noflight zone to enable a subsequently determined computation time tosatisfy the threshold, determine a buffer area surrounding the no flightzone, wherein the buffer area is defined by an offset distance from aperimeter of the no flight zone, construct a visibility graph includinglateral paths between the source point and the target point, the lateralpaths not passing through the no flight zone, the lateral pathsconnecting the first number of vertices or the second number of verticesof the no flight zone, the first number of vertices or the second numberof vertices taking into account the buffer area, and identify a firstlateral path of the lateral paths, the first lateral path being shorterthan others of the lateral paths.

Another example system includes memory storing computer readable codeand at least one processor to execute the computer readable code tocause the at least one processor to define an area between a sourcepoint and a target point, identify a first no flight zone within thearea, identify a second no flight zone outside of the area, estimate afirst computation time to determine a first lateral path for an aircraftto traverse between the source point and the target point, theestimating to consider the first no flight zone, the estimating not toconsider the second no flight zone, compare the first computation timeto a reference computation time, modify the first no flight zone to be athird no flight zone when the first computation time does not satisfy athreshold of the reference computation time, and estimate a secondcomputation time to determine a second lateral path for the aircraft totraverse between the source point and the target point, the estimatingto consider the third no flight zone.

Yet another example system includes memory storing computer readablecode and at least one processor to execute the computer readable code tocause the at least one processor to determine an initial path estimatebetween a source point and a target point associated with a flight of anaircraft, identify a first no flight zone and a second no flight zone,determine a first buffer area surrounding the first no flight zone and asecond buffer area surrounding the second no flight zone, wherein thefirst buffer area is defined by an offset distance from a perimeter ofthe first no flight zone and the second buffer area is defined by anoffset distance from a perimeter of the second no flight zone, identifyan overlap between the first no flight zone including the first bufferarea and the second no flight zone including the second buffer area,merge the first no flight zone including the first buffer area and thesecond no flight zone including the second buffer area into a third noflight zone including a third buffer area when the overlap isidentified, construct a visibility graph including lateral paths betweenthe source point and the target point, the lateral paths not passingthrough the third no flight zone including the third buffer area, thelateral paths connecting vertices of the third no flight zone, andidentify a first lateral path of the lateral paths, the first lateralpath being shorter than others of the lateral paths.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1. Shows an example flow diagram of a particular example of amethod for autonomous generation of shortest lateral paths for UnmannedAerial Systems (UAS) avoiding no-flight zones (NFZs). The flow diagramrepresents some example processes of the example method.

FIG. 2. Shows an example flow diagram of a particular example of thesub-processes relating to an example Heuristic process of FIG. 1.

FIG. 3. Shows an example flow diagram of example sub-processes of anexample Geodetic Layout Transformation process of FIG. 1.

FIG. 4. Shows an example flow diagram of example sub-processes of anexample Complexity Reduction process of FIG. 1.

FIG. 5. Shows an example flow diagram of a particular example of theprocesses that conform the example no-flight zones incursion process ofFIG. 1.

FIG. 6. Shows an example flow diagram of a particular example of theprocesses that conform the Lateral Path Definition process of FIG. 1.

FIGS. 7a and b . Show a particular example of a scenario in which theShortest Path Configuration Space (SPCS) has been defined. FIG. 7a showsan example geodetic scenario and FIG. 7b shows the example scenarioprojected in cartographic coordinates.

FIGS. 8a and b . Show a particular example of a scenario to which anexample simplification strategy is applied. Specifically, FIG. 8a showsan example Bounding Box strategy application and FIG. 8b shows anexample linear simplification strategy application.

FIG. 9. Shows the application of the example cutting bevel edge strategyto a particular no flight zone.

FIG. 10. Shows a particular example in which two no flight zones areoverlapped.

FIG. 11. Shows the example merging strategy applied to the particularexample of FIG. 10.

FIG. 12a . Shows particular examples in which the example convex hullalgorithm cannot be applied such that a potential path may be discarded.

FIG. 12b shows an example in which the target point may be discarded.

FIG. 13. Shows a particular example in which the example VisibilityGraph algorithm is applied to a particular Configuration Space (SPCS)including three no flight zones.

FIGS. 14 to 19. Show a particular example in which the example method ofthe present disclosure is applied to an example particular geodeticscenario.

DETAILED DESCRIPTION

A description of several examples of the present disclosure is carriedout, with illustrative character and without limitation, makingreference to the numbering used in the figures.

In a particular example of the disclosure, the method includes exampleprocesses that are shown in the flow diagram of FIG. 1. FIGS. 2 to 6show corresponding example processes of each main process of FIG. 1.

With reference to the example flow diagram of FIG. 1, after an initialand/or first scenario (1) is provided, the example method performs theexample “Heuristic process” (2). The example Heuristic process (2)assesses the initial scenario (1) to define a strategy (e.g., a strategythat enables some goals to be achieved such as, for example, reducingcomputation time and identifying a short lateral path) to find and/oridentify a feasible solution that takes into account computation timeand accuracy of the final lateral path. As shown in the example of FIG.2, the Heuristic process (2) includes three sub-processes:

As shown in FIG. 2, the first sub-process includes the Assessment of theScenario Geometry (10). This sub-process includes obtaining and/oraccessing some geometric information such as, for example, the Source(departure) and Target (destination) points (S&T) (12) and the existingno flight zones (13) from the initial scenario (1) to identify thecartographic projection (11) to reduce distortions at the overallscenario. Initially, in some examples, a majority of the scenarios aredefined in geodetic coordinates on the earth's surface and containinformation and/or data identifying and/or associated with the no flightzones. In some examples, the data identifying and/or associated with theno flight zones are related to the Shortest Path Configuration Space(SPCS) and/or the no flight zones are related to the Shortest PathConfiguration Space (SPCS). As used herein, the Shortest PathConfiguration Space is defined as the area of interest of the overallinitial scenario including the no flight zones disposed therein. In someexamples, no flight zones outside of the Shortest Path ConfigurationSpace, assuming that they exist, are clipped and/or removed fromconsideration to enable the examples disclosed herein to obtain arelatively more accurate estimation of the cartographic parametersand/or to enable the cartographic parameters to be more rapidlydetermined and/or defined. In such examples, the clipping and/or removalis executed after the scenario is translated into a cartographic plane.In some examples, the no flight zones outside of the Shortest PathConfiguration Space are removed from consideration using, for example,the cartographic projection in the ensuing first sub-process (e.g., FIG.2) of the second main process (FIG. 1). Thus, in the illustratedexample, the Heuristic process (2) makes a preliminary estimation of thescenario location and a geometric extension based on the no flight zones(e.g., all of the no flight zones within a particular area ofconsideration) and, optionally, the example Heuristic process makes asecond estimation once the no flight zones that are outside of theShortest Path Configuration Space have been clipped and/or removed fromconsideration. Based on the geometric information obtained, in theillustrated example, the example Heuristic process (2) defines acartographic projection (11) that, in some examples, will be used in theGeodetic Layout Transformation (3) process of FIG. 1 to translate theoriginal and clipped geodetic scenario into a cartographic scenario. Inthe illustrated example of FIG. 2, at the end of the Assessmentsub-process (10), the parameters that are used to define a cartographicprojection (11) for each scenario are identified. For example, scenarioswith no flight zones located in up to 10° to both sides of thesource/target segment defined between the source and target points (asegment joining points S&T) may be projected through an example ObliqueMercator Projection. However, in some examples, this projection may notbe directly applied on global scenarios (no flight zones located furtherthan 10° from the S&T segment) because distortion may be larger thanexpected.

In the illustrated example of FIG. 2, the second sub-process is theexample Estimation of the Computation Time (14). Based on previousanalysis of different scenarios, in some examples, some internalfunctions are built to estimate the overall computation time of themethod execution for each particular scenario. In some examples, thecomputation time is affected by: i) the number of no flight zones thatwill be potentially involved in the Shortest Path Configuration Space;ii) the efficiency of the implemented algorithms and; iii) thecomputational resources. Although the number of no flight zones, theefficiency of the implemented algorithms and the computational resourcesare not constants, the number of no flight zones, the efficiency of theimplemented algorithms and the computational resources may be relativelyprecisely estimated to define the internal function that will be used toestimate the expected computation time.

In the illustrated example of FIG. 2, the third sub-process is theStrategy Definition (15). This example sub-process (15) considers theestimated computation time previously obtained and the computation timerequirements (if the computation time requirements were previouslydefined) and finds and/or determines a feasible solution to meet suchtime. In other words, the strategy definition (15) determines a solutionthat enables a threshold to be met. In examples in which the estimatedtime is longer than required and/or if the estimated computational timedoes not satisfy a threshold of the desired computational time so theestimated computation time is not acceptable and/or does not satisfy thethreshold, an example Complexity Reduction process (4) of FIG. 1 overthe no flight zones is performed as detailed in the illustrated exampleof FIG. 4. If the example Complexity Reduction process (4) is performedbased on, for example, the estimated computational time not satisfyingthe threshold of the desired computational time, the example Heuristicprocess (1) selects a complexity reduction strategy to meet the requiredcomputation time. For example, the Heuristic process may select one of aplurality of complexity reduction strategies based on the ability of theone of the plurality of complexity reduction strategies enabling theestimated computational time to satisfy the threshold of the desiredcomputational time. In examples in which some of the no flight zones areremoved from consideration to decrease the estimated computational time,the example complexity reduction of the scenario may reduce the accuracyof the final path because some of the vertices that define the originalno flight zones will be removed and/or clipped from the scenario and/orfrom consideration. Hence, in some examples, the example Heuristicprocess (2) balances the computation time against the loss of accuracyin the final lateral path. Depending on the scenario and the context inwhich the example method is applied, in some examples, a faster solution(e.g., a faster computational time) may be preferred over a moreaccurate solution that takes longer (e.g., a slower computational time).As discussed in more detail below in FIG. 4, an example Bounding Boxstrategy and/or an example Linear simplification strategy may beselected by the Heuristic depending on the circumstances and/or theconstraints (e.g., computational time versus accuracy) of the problem.

As illustrated in the example of FIG. 1, the second main process of theexample method is the example Geodetic Layout Transformation (3). Insome examples, scenarios are defined in geodetic coordinates on theearth's surface, although they may alternatively be provided inCartesian coordinates. In examples in which the example scenario isprovided in Cartesian coordinates as opposed to geodetic coordinates,the example process of Geodetic Layout Transformation (3) may not beexecuted. Thus, in some examples, Geodetic Layout Transformation (3) isperformed when the example initial scenario provided includes geodeticcoordinates and not Cartesian coordinates. In some examples, determiningand/or solving the shortest lateral path problem on geodetic coordinatesuses relatively large amounts of computational resources. Thus, in someexamples, the shortest lateral path is determined in a planar domain. Asillustrated in the example of FIG. 1, the example Geodetic LayoutTransformation process (3) translates the initial geodetic scenario (1)into a Cartesian scenario and estimates the Projection Distortion Factor(PDF). The illustrated example of FIG. 3 shows the sub-processes of theexample Geodetic Layout Transformation process (3) of FIG. 1.

As illustrated in the example of FIG. 3, the first sub-process is theApplication of the Cartographic Projection (20). The example Applicationof the Cartographic Projection (20) applies the cartographic projectiondefined in the Heuristic process (2) of FIG. 1 to the overall initialscenario (1) to translate the geodetic coordinates into Cartesiancoordinates of the corresponding projection. Based on the processes ofthe Application Cartographic Projection (20), an initial planar scenario(21) is determined and/or generated. Referring to the example of FIG. 7a, a particular example of a geodetic scenario (60) includes a pluralityof no flight zones (61,62) and an unmanned aerial system (66) flyingfrom a source point (63) to a target point (64). The example S&T segment(65) joins, in geodetic coordinates, both the source and target points(63,64). The illustrated example of FIG. 7b shows the cartographictranslation of the geodetic scenario of FIG. 7a into Cartesiancoordinates.

Referring back to the illustrated example of FIG. 3, the secondsub-process is a Cartesian Clipping (22) applied on the initial planarscenario (21). The example process is performed by clipping and/or notconsidering some portions of the initial scenario and/or portionsoutside of the shortest lateral path where the shortest pathconfiguration space is defined as an area having no flight zone polygonsinvolved in the shortest lateral path definition. In some examples, toidentify such polygons, the example method assumes that: i) it ispossible to consider geodetic lines on the cartographic plane asstraight segments (instead of being curves), because the ProjectionDistortion Factor (PDF) is kept under a threshold tolerance value; andii) the cartographic projection used is conformal (angles on the earth'ssurface are preserved on the plane). In some examples, these assumptionsenable the complexity of the clipping problem to be reduced. Asillustrated in the example of FIG. 7b , the S&T segment (65) isconsidered as a straight segment and/or a substantially straight segmentenabling lines (67) that pass through S&T points (63,64) to berelatively easily defined. As illustrated example of 7 b, the lines (67)are substantially perpendicular relative to the S&T segment (65). Asshown in the example of FIG. 7b , the lines (67) define the approximatedearth's slice and/or an area that encloses the Shortest PathConfiguration Space (SPCS) (68). Given that the examples disclosedherein may be implemented in connection with unmanned aerial systemsthat tend to fly from a Source point to a Target points, no flight zones(NFZs) (61) behind those lines (67) may be disregarded. In other words,given that the examples disclosed herein are implemented with unmannedaerial systems that may not deviate between the source point and thetarget point, no flight zones outside of the source and target points,not between the source and target points and/or outside of a spacedefined between the source and target points may be disregarded whendetermining the shortest flight path and/or a flight path that satisfiesone or more thresholds (e.g., a threshold regarding computationaltime(s), a threshold regarding flight time, etc.). As a result, in someexamples, remote no flight zones (NFZs) (61) or no flight zones (61)outside of the area associated with the shortest path configurationspace (68) may not be considered and/or may be discarded from theoriginal scenario. In such examples, the initial number of no flightzones (NFZs) polygons is reduced and the extension of the scenario ischanged. Hence, in this example, the initial estimations made by theHeuristic process (2) is updated based on the shortest pathconfiguration space (68) and/or the no flight zones (61) outside ofand/or spaced from the shortest path configuration space (68).

In examples in which the scenario results are clipped and the number ofno flight zones (NFZs) are reduced (by deleting and/or not consideringno flight zone (NFZs) located outside the Shortest Path ConfigurationSpace (SPCS)), a second invocation of the example Heuristic process (23)is performed to update the cartographic parameters and the estimatedcomputation time of the scenario based on the new and/or updatedprojected and clipped scenario (e.g., an updated scenario, a secondscenario, etc.). In other words, the Heuristic process (23) process thedata after outlier no-fly zones are removed from consideration. Inexamples in which no flight zones (NFZs) are not located outside of theShortest Path Configuration Space (SPCS, the number of no flight zones(NFZs) remains the same before and after the cartesian clipping (22). Inother words, if there are zero no flight zones outside of the shortestpath configuration space (68), there are zero no flight zones to removefrom the problem being solved and, thus, the example method directlypasses to the example Estimation of the Projection Distortion Factor(PDF) sub-process (24) of FIG. 3.

As illustrated in the example of FIG. 3, the Estimation of theProjection Distortion Factor (PDF) sub-process (24) obtains and/oraccesses data and/or information associated with and/or regarding themaximum distortion produced on the no flight zones (NFZs) by thecartographic projection. Depending on the location of the no flight zonepolygons in the cartographic projection plane, in some examples, thedistortion factor is equal, greater or less than one. In some examples,distortion factors greater than one may be considered relevant for theexample method given that distance measures on the cartographic plane isa shortest geodetic distance on the earth's surface. For example, 1meter measure on the cartographic plane considering a ProjectionDistortion Factor (PDF) of 1.0001 corresponds to 0.9999 meters on theearth's surface. Therefore, in some examples, the Projection DistortionFactor (PDF) is used to define the safe distance in the no flight zoneincursion avoidance process (5) to substantially ensure a thresholddistance is maintained between the aircraft and the no flight zone. Inother words, the projection distortion factor affects the actualdistance between an aircraft (e.g., an unmanned aerial system) and a noflight zone. Thus, in accordance with the teachings of this disclosure,the determined projection distortion factor enables a threshold distanceto be maintained between the aircraft and no flight zones throughout amission between the source and target points.

Once the Shortest Path Configuration Space (SPCS) has been definedand/or determined (optionally it could be even more precisely defined inthe second iteration of the Heuristic process (23)) and the ProjectionDistortion Factor (PDF) has been estimated (24)), the next sub-processof the example of FIG. 3 is the example Validation of the CartesianScenario (25) (e.g., the validation of the planar scenario). In someexamples, to enable a scenario (e.g., an initial scenario, an updatedscenario, a clipped scenario, etc.) to be processed to identify theshortest path between the source and target points, the respectivescenarios are processed to determine if one or more thresholds aresatisfied. As shown in the example of FIG. 3, the validation of theCartesian scenario and/or planar scenario (25) determines and/oridentifies if the Source and Target points are inside of one of the noflight zone polygons (26). In examples in which the source and targetpoints are defined within a no flight zone polygon (26), the examplemethod may be unable to identify a route (e.g., a lateral path) thatdoes not pass through a no flight zone(s). Thus, in such examples, ifany of the S&T points (e.g., source and target points) are inside of anypolygon (e.g., the no flight zone polygons), then there are no lateralpaths available that do not violate the no flight zones (NFZs) and theexample method may not be applicable and/or the example method maysuggest an alternative source and/or target points (e.g., an alternativeroute) that do not violate the no flight zones. Secondly, as illustratedin the example of FIG. 3, the example method checks and/or processes thegeometry of the projected no flight zone (NFZs) polygons (27). In someexamples, depending on the shape of the polygons defined by the noflight zones, examples disclosed herein may simplify the shape of thepolygon to increase the speed at which processing can occur. Forexample, the examples disclosed herein may simplify and/or reduce thecomplexity of a polygon by removing holes disposed within a boundary ofthe no-fly zone polygon, combining polygons that intersect one anotherand/or reducing the complexity of the shape of a polygon by removingvertices should, for example, the polygon intersect itself. If themethod determines that the complexity of the polygons is relativelyhigh, the example method may apply an example simplification algorithmto the no flight zone contours. In such examples, the examplesimplification algorithm may reduce the complexity of the no flight zonepolygon, thereby reducing the complexity of the problem being solved.Thirdly, the example method checks and/or determines whether theProjection Distortion Factor (PDF) has a reasonable value (28) and/orwhether or not the projection distortion factor satisfies a threshold.In some examples, determining that the projection distortion factorsatisfies the threshold includes determining that the distortion for thespecific scenario is feasible. In some examples, a reference ProjectionDistortion Factor (PDF) threshold is established and/or defined andcompared to the reference Projection Distortion Factor (PDF) todetermine whether the determined projection distortion factor satisfiesa threshold of the reference projection distortion factor. In someexamples, at the end of the validation sub-process (26), the outcomewill be the portion of the planar scenario corresponding to the ShortestPath Configuration Space (SPCS) including a set of no flight zone planarpolygons inside the Shortest Path Configuration Space (SPCS).

As illustrated in the example of FIG. 1, the third main process includesa Complexity Reduction (4). In the illustrated example, the overallnumber of vertices that defines the no flight zones (NFZs) is used toobtain a solution that meets and/or satisfies a threshold response time(e.g., a required response time). In some examples, the complexityreduction process (4) applies different vertex reduction strategies tosimplify the geometry of the no flight zone polygons to reduce theoverall computation time in processes and, more generally, to decreasethe computation time of the examples disclosed herein. Some exampleprocesses associated with the complexity reduction (4) are performedwhen the estimated computation time to obtain the shortest lateral pathdoes not satisfy a threshold and/or the estimated computation time ishigher than a threshold value (e.g., a required time). In examples inwhich the estimated computation time satisfies a threshold, then theplanar no flight zone polygons may be directly considered as thesimplified planar no flight zone polygons. In some examples, reducingthe number of vertices defined by a no flight zone may reduce theaccuracy of the obtained lateral path given that the examples disclosedherein use the no flight zone vertices to determine and/or identify thelateral path. However, in some examples, having a greater number ofvertices define the no flight zone may increase the computation time toidentify a lateral path having higher precision and/or accuracy. Thus,constraints of processing time and accuracy of the lateral pathidentified are considered and/or weighted when approaching a particularproblem. Given the balancing between processing time and the accuracy ofthe lateral path identified, in the illustrated example, the exampleheuristic process (2,23) balances between meeting the thresholdcomputation time (e.g., the required computation time) and the number ofvertices and recommends a suitable reduction strategy that provides, forexample, the highest level of accuracy while satisfying the thresholdcomputation time. As shown in the illustrated example of FIG. 4, themethod applies the example reduction strategy over the planar no flightzone polygons (30) inside the Shortest Path Configuration Space (SPCS)to obtain a set of Simplified Planar no flight zone polygons (33). Insome examples, two possible reduction strategies are considered:

As illustrated in the example of FIG. 4, the example Bounding Boxsimplification strategy (31) bounds all the polygons by rectangularareas reducing the number of vertices to four times the number of noflight zones (NFZs). In other words, the Bounding Box simplificationstrategy (31) defines four vertices per no flight zone. Examplesimplementing the example Bounding Box simplification strategy (31) mayreduce the amount of computation time at the expense of accuracy in thelateral path identified and/or the lateral path solution. The example ofFIG. 8a shows the application of the example Bounding Box simplificationstrategy to a particular no flight zone (69). As shown in the example ofFIG. 8a , the Bounding Box simplification strategy defines a four sidedbox (70) with dimensions corresponding to the longer distances of theinitial planar no flight zones (NFZ).

As illustrated in the example of FIG. 4, the Linear Simplificationstrategy (32) is based on an example customized Douglas-Peuckeralgorithm. In some examples, the Linear Simplification strategy (32)uses an internal distance, which is defined as Linear Distance (LD),between the sides of the planar no flight zone polygons (30) and thecorresponding sides of the simplified Planar no flight zone polygons(33) to reduce the number of vertices. The example of FIG. 8b shows theresulting simplified polygon no flight zone (71) obtained by applyingthe example customized Douglas-Peucker algorithm on the same polygon noflight zone (69) of FIG. 8a . A shown in FIG. 8b , the example methodselects and keeps the maximum linear distance (LD) distance among theobtained linear distances (72). In some examples, the exampleDouglas-Peucker algorithm balances between the complexity reduction,computation time and accuracy of the path. In some examples, the lineardistance threshold (LDT) is equal to 0 if the Bounding Boxsimplification strategy (31) is applied.

In the illustrated example of FIG. 1, the fourth main process is theexample no flight zone Incursion Avoidance (5). In some examples, the noflight zone incursion avoidance (5) offsets a safe distance to theSimplified Planar no flight zone Polygons (33) coming from the previousprocess (e.g., the complexity reduction process (4)). As shown in FIG.5, the no flight zone incursion avoidance process (5) comprises thefollowing sub-processes:

As illustrated in the example of FIG. 5, the example Estimation of theOffset Distance (40) calculates a safe buffer distance to avoid noflight zone (NFZs) incursions considering all and/or substantially allinfluence factors that can and/or may contribute to the unmanned aerialsystem entering the no flight zones (NFZs). In some examples, the safebuffer distance is defined to prioritize no incursions on the no flightzones (NFZs), which implies emphasis of the considered influencefactors. Thus, in such examples, the shortest paths may be consideredconservative from a safety perspective and hence, will be pseudo-optimalwith regard to the real geodetic distance. In some examples, thefollowing factors are considered to influence the offset distance: i)the Projection Distortion Factor (PDF) (41) previously estimateddistorts the real geodetic distances; thus, the offset distance measurein the plane are not realistic on the earth surface; ii) the LinearSimplification shifts the boundaries of the no flight zones (NFZs)towards its interior, at most, the linear distance (LD) (42), thus, theLinear Distance (LD) are amended; iii) the worst unmanned aerial systemTurn Radius (TR) (43), a less desirable turn radius (43) and/or a turnradius that does not satisfy a threshold is also a factor to consider;iv) the Position Uncertainty (PU) (44) of the unmanned aerial system,which primarily depends on the navigation capabilities of the unmannedaerial system. The following example expression considers these factorsto estimate a safe offset distance:

Offset distance(OD)=PDF*(LD+TR+PU)

In some examples, a Constant offset Distance (CD) may be added to ensureand/or enable a minimum distance from the no flight zones (NFZs) to beachieved. In such examples, the final estimation of the offset distanceshould be:

Offset distance(OD)=PDF*(LD+TR+PU+CD)

The Application of the Offset Distance (45) shifts the no flight zonepolygons' boundary (73) outwardly by the specific offset distance (OD)(75) calculated in association with the Estimation of the OffsetDistance process (40). Based on the process of the application of theoffset distance (45), results in a set of offset planar no flight zones(NFZs) (74). In examples in which any of the angles of the offset noflight zone polygons (74) is very acute and/or relatively large, the noflight zone polygons (74) are bevel cut (46) to increase theConfiguration Space and avoid and/or deter missing potential lateralpaths, as shown in the example of FIG. 9. As illustrated in the exampleof FIG. 9, the cropped area (76) remains outside the simplified andoffset planar no flight zone polygons (47).

In some examples and as illustrated in the example of FIG. 10, as aresult of applying the offset distance, some no flight zone polygons(77,78), with their respective offset areas (79,80) surrounding them,may overlap. In examples in which two no flight zone polygons (77, 78)are identified as intersecting and overlapping, the no flight zonepolygons (77, 78) can be merged (48) to create a new simplified noflight zone polygon (49) with a single offset area (81), as is shown inFIG. 11.

Referring back FIG. 1, at the end of the example no flight zoneincursion avoidance process (5), a set of Simplified, Offset & MergingPlanar no flight zone Polygons (49) are obtained.

In the illustrated example of FIG. 1, the fifth main process is theexample Lateral Path Identification process (6). In some examples, thelateral path identification process (6) finds the pseudo-optimalshortest path distance between the Source and Target points. Asillustrated in the example of FIG. 6, the lateral path definition (6)comprises the following sub-processes:

Referring to FIG. 6, a first sub-process is the application of anexample Visibility Graph algorithm (51) to the Shortest PathConfiguration Space (SPCS) to find all and/or substantially all thepossible lateral paths between the S&T points (e.g., source and targetpoints). In some examples, the visibility graph algorithm finds theshortest path through the convex hull polygons' boundaries. In thisexample, the input for this sub-process is the example Simplified,Offset & Merging cartographic no flight zone polygons (49) coming fromthe previous process. Therefore, in some examples, the first internalsub-process is the application of a Convex Hull algorithm (50). In someexamples, the convex hull algorithm is not applied in cases in which thesource and target points or any other point of a no flight zone isenclosed within the convex hull areas of another no flight zone (NFZ),because in these cases the potential shortest paths may be discarded,for example. The example of FIG. 12a shows a particular case in whichthe example Convex hull algorithm modifies (see dashed line (84)) theperimeter of a first no flight zone (NFZ1) (82) in such a way that thefirst no flight zone NFZ1 (82) and a second no flight zone NFZ2 (83)overlap, thereby closing the space between both no flight zones (82,83)and discarding a potential shortest path. In other words, in someexamples, when two no flight zones have perimeters that overlap and/orhave profiles that interrelate (e.g., a first no flight zone defining aconcave perimeter portion into which a convex perimeter portion of asecond no flight zone is positioned), the example convex hull algorithmmay modify the boundary of the no flight zone by directly intersectingvertices that were previously not directly connected by a single line(84). The example of FIG. 12b shows another particular case in which thetarget point (85) falls within the convex hull polygons' boundaries. Insuch an example, if the convex hull algorithm is applied, the method maynot find a solution given that the target point (85) is disposed withinthe no flight zone (82).

Referring back to FIG. 6, after the application of the example ConvexHull algorithm (50), in the illustrated example, the Visibility Graphalgorithm (51) is applied to identify all and/or substantially alllikely geometric paths between S&T points (e.g., the source and targetpoints), as shown in FIG. 13. FIG. 13 shows three Simplified, Offset &Merging cartographic no flight zone polygons (86,87,88) where the dashedlines represent the offset areas surrounding the no flight zones (NFZs))and an unmanned aerial system(89) trying to arrive to a target point(90) from a source point (91). Thus, the examples disclosed hereinidentify points between the source and target points that do not passthrough one of the no flight zones including the safety buffersurrounding and/or adjacent to the respective no flight zone. Theexample algorithm (51) identifies the visible connections among theoverall set of points of the Shortest Path Configuration Space (SPCS).In some examples, if the line segment connecting two points (orlocations) does not pass through any obstacle, a new edge between themis created and added to the graph. As shown in the example of FIG. 13,these line segments (92) connect the source and target points with thevertex of the offset areas. These line segments (92) are representedwith solid lines in FIG. 13. In addition, in some examples, the lengthof each edge is calculated (either Euclidean or Geodetic distances) andadded as an edge attribute that can be used to identify the shortestpath distance.

Referring to the example of FIG. 6, once the visibility graph has beenbuilt, the next sub-process is the execution of Dijkstra's algorithm(52) that finds the path with lowest cost (i.e. shortest path distance)between the source and target points.

The example method then selects the cartographic set of waypoints thatdefines the shortest path (53) and the waypoints are then translated togeodetic coordinates (54) to define a geodetic pseudo-optimal shortestpath. Finally, in the illustrated example, the geodetic path defined bywaypoints is obtained (55) and the unmanned aerial system will fly thecreated geodetic shortest lateral path.

In some examples, the obtained shortest lateral path is consideredpseudo-optimal for two reasons. For example, the first reason is becauseworking with planar coordinates without distortion can assure that theobtained path is the shortest one and the second reason is that thepolygon simplification and offset addition necessarily introduce somedistortions that affects the path obtained.

While the examples disclosed above mention no flight zones positionedwithin the shortest Path configuration space, the method is configuredto identify the shortest lateral path even when there is no flight zoneinside the Shortest Path Configuration Space (SPCS) since the shortestlateral path will be the straight line.

The examples of FIGS. 14 to 19 show a particular example of the methodapplied to a specific scenario. The example scenario (100) in geodeticcoordinates, as shown in FIG. 14, has a Shortest Path ConfigurationSpace (SPCS) (101) delimited between the Source (S) and Target (T)points, the points (T, S) defining the flight intention vector (104) of,for example, a unmanned aerial system platform (105). The example methodfirstly executes the heuristic process (2) analyzing the initialgeodetic scenario (100). As a result of this example heuristic process,the example method obtains a cartographic projection of the initialgeodetic scenario (100). In some examples, the Shortest PathConfiguration Space (SPCS) (100) comprises a first set of no flightzones (NFZs) (102) potentially involved in the lateral path solutionthat are considered. As illustrated in FIG. 14, there is a second set ofno flight zones (NFZs) (103) located outside of the Shortest PathConfiguration Space (SPCS) (101) that will be clipped and/or notconsidered to reduce the complexity of the initial geodetic scenario.After the application of the geodetic layout transformation (3) to theoriginal geodetic scenario (1), in this example, an originalcartographic scenario (106) is obtained, as shown in FIG. 15. Thecartographic scenario (106) focuses on the no flight zones (107-113)potentially involved in the lateral path solution. Since the scenariohas been clipped to remove the no flight zones (103) that are outside ofthe shortest Path configuration space (100), the second set of no flightzones (103) has been discarded, in this example, the heuristic processis executed again over the clipped planar scenario (106). The examplemethod estimates a computation time that is used to obtain a lateralpath solution and compares the estimated computation time with areference computation time (e.g., a required computation time that hasbeen previously defined). In this example, a linear simplificationstrategy is selected to reduce the estimated computation time. Then, theexample method calculates the Projection Distortion Factor (PDF) andchecks: i) that the Source and Target points are outside of any noflight zone (NFZ); there are no complex polygons; and the ProjectionDistortion Factor (PDF) obtained satisfies a threshold and/or is under apredefined threshold. The selected linear simplification strategy isapplied comprising an example tailored Douglas-Peucker algorithm thatsimplifies the polygons by reducing the number of vertices of therespective polygons (the resulting no flight zone polygons are markedwith dashed lines in FIG. 15). Then, in some examples, the maximumlinear distance (LD) is calculated.

The illustrated example of FIG. 16 shows the simplified no flight zonepolygons (107-113) to which the safety area is added. In this example,the dashed line surrounding each no flight zone (107-113) represents thesafety area. The safety area is defined by the Projection DistortionFactor (PDF), the Linear Distance and the Turn Radius of the unmannedaircraft (105) and the Position Uncertainty introduced by the onboardnavigation system. As shown in the example of FIG. 16, the safety areasof the no flight zones (NFZs) (107,108) and the no flight zones (NFZs)(111,113) overlap, so in accordance with the teachings of thisdisclosure, the no flight zones (107, 108) are merged as shown in FIG.17 and the no flight zones (111, 113) are merged as shown is FIG. 17.Optionally, in some examples, the method may cut bevel edges of any ofthe no flight zones. In this example, the example convex hull algorithmis applied to find, determine and/or identify the shortest path throughthe example convex hull polygons' boundaries. The illustrated example ofFIG. 17 shows the result of the example convex hull algorithmapplication to the scenario (104) where the safety area of the merged noflight zone (107,108), merged no flight zone (111,113) and the no flightzone (109) is modified, see dashed-dotted line.

As illustrated in FIG. 17, the no flight zones (NFZs) are shown with theresulting safety areas surrounding them in dotted lines. In someexamples, the safety areas defined by the dotted lines surrounding theno flight zones substantially ensure that the unmanned aerial systemdoes not deviate into the respective no flight zones. The example methodapplies the example Visibility Graph algorithm that identifies alland/or substantially all likely geometric paths between the Source andTarget points. As illustrated in FIG. 17, the geometric paths identifiedconnect safety areas' vertices and avoid passing over any of the noflight zones (NFZs). The example method identifies the shortest lateralpath (114) by applying the example Dijkstra's algorithm as shown in FIG.19. The cartographic set of waypoints that defines the shortest path istranslated into geodetic coordinates to define a geodetic pseudo-optimalshortest path that is sent to a trajectory generator of the unmannedaircraft. Based on the processes performed in accordance with thisdisclosure and the path identified that balances computational timewhile avoiding no flight zones, the unmanned aircraft (105) files theobtained geodetic shortest lateral path (114).

The present disclosure relates to a method and a system for autonomousgeneration of shortest lateral paths for Unmanned Aerial Systems (UAM)that avoids no-flight zones (NFZs). The disclosure proposes a safe,practical and robust solution for autonomously generating geodeticpseudo-optimal lateral paths for unmanned aerial systems while avoidingno flight zones (NFZs) and taking into account computational timerequirements and computational capabilities to obtain the best possiblesolution that satisfies the time threshold. The method underlies aneffective sequence of processes that combine heuristic, geodetic andgeometric algorithms to provide an efficient and robust solution formost common unmanned aerial system scenarios.

Autonomous generation of unmanned aerial system flight lateral pathswith no intervention from a remote pilot still represents a majorchallenge in unmanned aerial systems. Limited onboard computationalcapabilities, high complexity of geodetic scenarios, numerous no flightzones (NFZs) and crowded airspace are some of the issues that stillmakes this problem difficult. Scenarios in the unmanned aerial systemdomain are frequently an extensive number of geodetic no flight zonepolygons that can be located anywhere in the world, with any extension,with very complex shapes being defined by a large number of vertices.For example, boundaries of the most common geographic features likecities or airports are commonly considered as no flight zones (NFZs).This makes the geodetic identification of the shortest path in extensiveareas on the earth's surface, while avoiding no flight zones (NFZs), anissue some examples do not address.

Some of the specific issues associated with the generation of a shortestlateral path for unmanned aerial system are the following:

-   -   each particular unmanned aerial system platform has specific        performance characteristics and limitations that are considered        to provide safe and flyable trajectories;    -   the predictability of vehicle motion and, thus, its position        accuracy are subjected to high uncertainties;    -   unmanned aerial system scenarios usually comprise a large number        of no flight zones (NFZs) with complex geometries that require        extensive computational resources and time to be executed,        especially under the limited computational resources of the        common unmanned aerial system onboard computers. In addition,        the operational real-time requirements of the unmanned aerial        system missions are also limited; and,    -   unmanned aerial system operational scenarios are located        anywhere in the world and may have any extension. Defining        scenarios on a geodetic datum (e.g. WGS84) increases the        complexity of the shortest lateral path solution. Solving the        complete geodetic problem in ellipsoidal geometry requires        complex geodetic algorithms and extensive computational        resources.

The examples described herein consider the cited problems associatedwith the particularities of the autonomous trajectory definition inunmanned aerial system operational scenarios and provide an autonomousdefinition of a geodetic pseudo-optimal shortest lateral path forunmanned aerial system avoiding no flight zones (NFZs), that can bedefined anywhere in the world and have any geographical extension.Furthermore, the disclosed examples provide improved results within arequired time range. The examples grant a safe and robust unmannedaerial system trajectory and provide a balance between computationalefficiency and solution accuracy.

An example method of autonomous generation of shortest lateral path forUnmanned Aerial Systems (UAM), wherein a constant Turn Radius (TR) and aconstant vertical path of a unmanned aerial system platform ispreviously defined, comprises receiving an initial scenario defined incartographic coordinates, the initial scenario comprising a source pointand a target point that define a vector representing an initial flightintention of the unmanned aerial system platform and at least one NoFlight Zone (NFZ); determining a computation time for obtaining ashortest lateral path that avoids the at least one no flight zone (NFZ),the computation time being proportional to an overall number of verticesof the at least one no flight zones (NFZ), determining whether thedetermined computation time is less than or equal to a predeterminedrequired computation time; determining a safety area surrounding eachindividual no flight zone (NFZ), wherein the safety area is defined byan offset distance from the perimeter of the safety area; constructing avisibility graph comprising all the possible lateral paths between thesource point and the target point avoiding the no flight zones (NFZs),the possible lateral paths being all possible combinations of vectorsconnecting the vertices of the safety zones; and determining theshortest lateral path among all the possible lateral paths constructedin the visibility graph.

In some examples, when the initial scenario is defined in geodeticcoordinates, the method comprises: defining a cartographic projection ofthe initial scenario considering a geometric extension and a geographiclocation of the initial scenario; and translating the initial scenariodefined in geodetic coordinates into an equivalent initial scenariodefined in cartographic coordinates by applying the defined cartographicprojection to the initial scenario defined in geodetic coordinates.

In some examples, the method includes determining a configuration spaceas an area delimited by two perpendicular lines to the initial flightintention vector, each perpendicular line passing through one of thesource and the target points respectively; and, discarding any noflights zone located outside the Configuration Space.

In some examples, when at least one no flight zone has been discardedand at least one of the no flight zones (NFZs) is located inside theConfiguration Space, the method further comprising considering only theno flight zones (NFZs) inside the Configuration Space; re-determining acomputation time for obtaining a shortest lateral path that avoids theat least one no flight zone (NFZ); re-determining a safety areasurrounding each individual no flight zones (NFZ); re-constructing avisibility graph; and re-determining the shortest lateral path among allthe possible lateral paths.

In some examples, the method includes determining a scale factorintroduced by the translation of the initial scenario defined ingeodetic coordinates into the equivalent initial scenario defined incartographic coordinates. In some examples, when the determinedcomputation time exceeds the required computation time, the methodcomprising reducing a total number of vertices of the safety areas byapplying a vertex reduction algorithm to each safety area. In someexamples, the vertex reduction algorithm is performed using at least oneof a minimum Bounding Box algorithm or a linear simplificationalgorithm.

In some examples, determining a safety area surrounding each individualno flight zone further comprises cutting bevel edges of angled portionsof the safety areas, where the angled portions have an angle less than apredefined angle threshold. In some examples, determining a safety areasurrounding each individual no flight zone further comprises mergingoverlapped safety areas of contiguous no flight zones (NFZs).

An example system for autonomously generating shortest lateral path forUnmanned Aerial Systems (UAM) comprises: memory storing an autonomouslateral path generator configured to receive an initial scenario incartographic coordinates, the initial scenario comprises at least one noflight zone and a source and a target point that determine an initialflight intention vector of the unmanned aerial system platform; and aprocessor configured execute the lateral path generator to: determine acomputation time to obtain a shortest lateral path avoiding the noflight zones (NFZs), the computation time being proportional to anoverall number of vertices of the no flight zones (NFZs); determinewhether the determined computation time is less than or equal to apredetermined required computation time; determine an offset distance,to create a safety area surrounding each no flight zone where the safetyarea is defined by the safety offset distance and redefining theperimeter of each no flights zone by including such safety area; createa visibility graph with all possible lateral paths between the initialand target points that avoid the redefined no flight zones (NFZs), thepossible lateral paths being all possible combinations of vectorsconnecting the vertices of the safety areas; and determine the shortestlateral path among all generated lateral paths.

In some examples, the lateral path generator is further configured todefine a cartographic projection of the initial scenario defined ingeodetic coordinates and translating the initial scenario into aninitial scenario defined in cartographic coordinates by applying thecartographic projection to the initial scenario. In some examples, thelateral path generator is further configured to determine aConfiguration Space as an area delimited by two perpendicular lines tothe initial flight intention vector, each perpendicular line passingthrough the source and target points respectively, and identify anddiscard any no flight zone located outside the Configuration Space.

In some examples, the lateral path generator is further configured toestimate a scale factor introduced by the translation of the initialscenario defined in geodetic coordinates into the initial scenariodefined in cartographic coordinates. In some examples, the lateral pathgenerator is further configured to determine whether the Source andTarget points are located outside any safety area and further determinea Projection Distortion Factor as a minimum scale factor that ensuresthe safety offset distances are always equal or larger than apredetermined minimum safety distance. In some examples, the lateralpath generator is further configured to reduce a total number ofvertices of the no flight zones (NFZs) by applying a vertex reductionalgorithm to each no flight zone (NFZ).

An example computer program product for autonomously generating ashortest lateral path, the computer program product comprises: acomputer-readable storage medium having computer-readable program codeembodied therewith, the computer-readable program code executable by oneor more computer processors to: determine a computation time to obtain ashortest lateral path avoiding the no flight zones (NFZs), thecomputation time being proportional to an overall number of vertices ofthe no flight zones (NFZs); determine whether the determined computationtime is less than or equal to a predetermined required computation time;determine an offset distance, to create a safety area surrounding eachno flight zone where the safety area is defined by the safety offsetdistance and redefining the perimeter of each no flight zone byincluding such safety area; create a visibility graph with all possiblelateral paths between the initial and target points that avoid theredefined no flight zones (NFZs), the possible lateral paths being allpossible combinations of vectors connecting the vertices of the safetyareas; and determine the shortest lateral path among all generatedlateral paths.

The example methods and systems disclosed herein relate to autonomouslygenerating shortest lateral paths for Unmanned Aerial Systems (UAS) thatavoids no-flight Zones (e.g., NFZs, no-fly zones) while taking intoaccount computational time requirements and computational capabilitiesto satisfy a threshold, obtain optimal and/or beneficial real timesolutions. As defined herein, the no flight zones and/or no-fly zonesare territories or areas over which aircraft are not permitted to fly.The examples disclosed herein include an example method of autonomousgeneration of a shortest and/or lesser lateral path for Unmanned AerialSystems (UAS) where a constant Turn Radius (TR) and a constant verticalpath of an unmanned aerial system platform is previously defined and/orknown. The example method includes the processes of receiving exampleinitial and/or a first scenario defined in cartographic coordinateswhere the first scenario includes a first Source point and a firstTarget point that define a first vector representing an example initialand/or first flight intention of the unmanned aerial platform and atleast one no flight zone (NFZ). In some examples, the example methodincludes estimating a first computation time for obtaining the shortestand/or a lesser lateral path that avoids the no flight zone(s) where thefirst computation time (e.g., the required computation time) is directlyproportional to an overall number of vertex of the no flight zone(s). Insome examples, the method includes comparing the estimated firstcomputation time to a reference computation time (e.g., a computationtime previously provided) to determine that the estimated firstcomputation time is less than or equal to the reference computationtime.

In some examples, the method also includes determining a safety areasurrounding each no flight zone where the safety area is defined by anoffset distance; and constructing a visibility graph and/or an examplegraph that includes all and/or substantially all possible lateral pathsbetween the first Source point and the first Target point that avoidand/or substantially avoid the no flight zone(s). In some examples, thepossible lateral paths include all and/or substantially all possiblecombinations of vectors connecting the vertices of the safety zones. Insome examples, the method includes determining the shortest lateral pathamong all the possible lateral paths generated in the visibility graph.

In some examples, when the first scenario is defined in geodeticcoordinates instead of cartographic coordinates, the example methoddefines a first cartographic projection of the first scenarioconsidering a first geometric extension and a first geographic locationof the first scenario; and translates the first scenario defined ingeodetic coordinates into an equivalent initial and/or second scenariodefined in cartographic coordinates by applying the defined cartographicprojection to the first scenario defined in geodetic coordinates.

Advantageously, in some examples, to reduce the complexity of thelateral path calculation, the example method determines a configurationspace as an area delimited by and/or bounded by two perpendicular and/orsubstantially perpendicular lines. As used herein, substantiallyperpendicular means within about fifteen degrees of perpendicular. Insome examples, each perpendicular and/or substantially perpendicularline passes through the first Source point and first Target pointrespectively, to the initial and/or first flight intention vector; and,discards and/or does not consider any no flight zones located outsidethe configuration space.

In some examples, when at least one no flight zone has been discardedand at least one of the no flight zones is located inside theconfiguration space, the method further includes determining theshortest lateral path considering only the no flight zones inside theconfiguration space. In other words, the example method may not considerno flight zones outside of the configuration space

The example method estimates a first scale factor for each point of thesecond scenario that is introduced by the translation of the firstscenario defined in first geodetic coordinates into the second scenariodefined in cartographic coordinates. In some examples, the first scalefactor is a variable parameter that depends on the longitude andlatitude values of the different points of the geodetic scenario andrepresents a measure of the distortion introduced by the cartographicprojection.

In some examples, the method checks that the first Source and firstTarget points are located outside any surrounding safety areas of the noflight zones and estimates a first Projection Distortion Factor (PDF) asthe minimum scale factor that ensures and/or substantially ensures thatthe safety offset distance is always equal or larger than a minimumsafety distance. This projection distortion factor will be the scalefactor that assures that none of the safety offset distances in thedefined cartographic plane will be lesser than a minimum safety distanceestablished in the geodetic ellipsoid. In other words, the examplesdisclosed herein ensure and/or substantially ensure that unmanned aerialvehicles maintain a distance from no flight zones and/or maintain aminimum distance from a safety offset of the respective no flight zones.

In some examples, when the estimated computation time exceeds therequired computation time, the method reduces the total number ofvertices of the safety areas by applying an example vertex reductionalgorithm to each safety area. In some examples, this example vertexreduction algorithm is selected between an example minimum Bounding Boxalgorithm and an example linear simplification algorithm. When theexample linear simplification algorithm is selected, in some examples,the method applies an example tailored Douglas-Peucker algorithm to eachno flight zone determining a maximum Linear Distance (LD) thatcorresponds to a largest simplification distance between each originalno flight zone or the corresponding simplified no flight zone.

In some examples, the Offset Distance employed in determining the safetyarea is calculated by the following expression:

Offset distance=PDF×(TR+PU)

where PDF is the Projection Distortion Factor, TR is the Turn Radius ofthe unmanned vehicle system platform and PU is a Position Uncertaintyvalue of the unmanned vehicle system platform. In examples in which thelinear simplification algorithm is applied to the safety areas, theOffset Distance is calculated by the following expression

Offset distance=PDF×(TR+PU+LD)

where LD is the maximum Linear Distance.

In some examples, a constant safety area may be introduced to increasethe security distance between the unmanned aerial system and the no-flyzones, so the offset distance can be calculated by the followingexpression:

Offset distance=PDF×(TR+PU+LD+CD)

where CD is the Constant Safety Distance added to the Offset Distance.

In some examples if the first scenario is directly provided incartographic coordinates, so there is no need of a cartographicprojection, the offset distance will be calculated as the sum of theTurn Radius plus the Position Uncertainty value and eventually plus theConstant Safety Distance and/or the Linear Distance.

In some examples, determining a safety area surrounding each individualno flight zone includes cutting bevel edges of angled portions of thesafety areas, where the angled portions have an angle less than apredefined angle threshold. Preferably, in some examples, the anglethreshold might be any possible angle between 0 and 90 degrees.

In some examples, determining a safety area surrounding each individualno flight zones further includes merging overlapped safety areas ofcontiguous no flight zones. In other words, a safety area may includetwo or more no flight zones that are near and/or immediately adjacentone another and/or the safety area may encompass multiple no flightzones.

In some examples, determining a safety area surrounding each individualno flight zone and/or surrounding multiple no flight zones includesapplying an example convex hull algorithm to the safety areas forsimplifying the resulting no flight zone polygons.

In some examples, the present disclosure provides an example system forautonomously generating shortest lateral path for unmanned aerialsystems that avoids no flight zones. The system includes an exampleautonomous lateral path generator configured to receive an initialand/or first scenario in cartographic coordinates, the first scenarioincludes at least one no flight zone and a first source and a firsttarget point that determine and/or define an initial and/or first flightintention vector of the unmanned aerial system platform; means fordetermining a first estimated computation time for obtaining theshortest lateral path between the first source point and the firsttarget point that avoids the no flight zones, the first estimatedcomputation time being directly proportional to an overall number ofvertex of the no flight zones, and checking that the estimatedcomputation time is less than or equal to a reference computation timeand/or required computation time previously provided; means fordetermining an offset distance, creating a safety area surrounding eachno flight zone where the safety area is defined by the safety offsetdistance and redefining the perimeter of each no flight zone byincluding such safety area and/or changing a first perimeter of a firstno flight zone to be a second perimeter greater than the first perimeterwhere the second perimeter includes the safety area. In some examples,the example system includes means for creating a visibility graph withall possible lateral paths between the initial, source and/or targetpoints that avoid the redefined no flight zones, the possible lateralpaths being all possible combinations of vectors connecting the verticesof the safety areas; and the example lateral path generator beingfurther configured to determine the shortest lateral path among allgenerated lateral paths. In other words, the examples disclosed hereindetermine a short and/or shortest path of a mission by identifying afirst no flight zone and including a safety buffer about the firstflight zone such that the first no flight zone is a second no flightzone that is larger than the first no flight zone where the second noflight zone includes the safety buffer.

Advantageously, in some examples, the example system includes means fordefining a cartographic projection of the initial scenario defined ingeodetic coordinates and translating the initial scenario into anequivalent initial scenario defined in cartographic coordinates byapplying the cartographic projection to the initial scenario.

In some examples the example system further comprises means fordetermining a configuration space as an area delimited by twoperpendicular and/or substantially perpendicular lines, where eachperpendicular line passing through the first Source point and firstTarget point respectively, to the initial flight intention vector; andmeans for identifying and discarding any no flight zone located outsidethe Configuration Space.

The example system includes means for estimating a scale factorintroduced by the translation of the first scenario defined in geodeticcoordinates into the second scenario defined in cartographiccoordinates. In some examples, the first scenario defined by thegeodetic coordinates is substantially similar to the second scenariodefined in cartographic coordinates.

In some examples, the example system includes means for checking thatthe first Source point and first Target point are located outside anysafety area and means for estimating a Projection Distortion Factor asthe minimum scale factor that ensures that the safety offset distancesare always equal or larger than a minimum safety distance.

In some examples, the example system reduces a total number of verticesof the no flight zones by applying an example vertex reduction algorithmto each no flight zone. In some examples, the vertex reduction algorithmis preferably selected between a Bounding Box algorithm and a linearsimplification algorithm.

Some of the advantages of the present disclosure include the ability toconsider geodetic issues related to distortions as well as scenarios inplanar coordinates. Thus, in some examples, a simplification of thetechnical problem is herein described. The examples disclosed hereinwork with geodetic scenarios and consider issues related to distortionsto provide a more accurate solution. To do that, in some examples, thecartographic projection is autonomously selected to better reduce thedistortion factors which is a technical difference with some examples.

The example systems and methods enable the handling of any type ofgeometric scenarios with no limitation regarding their extension, numberof no flight zone polygons, shape or location of both the no flightzones and the first Source and first Target points.

The example method also includes an example clipping task to select theno flight zones directly related to the shortest path problem. Such anapproach enables the reduction of the complexity of the scenarios.

The example systems and methods consider as input a computational timerequirement in which a possible resulting path is to be found. Then, insome examples, the systems and methods estimate the expected computationtime for the input scenario and decides, identifies and/or determines anexample simplification strategy to meet such time requirement. As aconsequence, in some examples, a pseudo-optimal shortest path isobtained. Some examples solutions do not consider a computational timerequirement, which is an important drawback that could put at risk theunmanned aerial systems mission.

Using the examples disclosed herein, assumptions about the scenario havebeen reduced as much as possible to provide a robust solution for anyscenario. In contrast, some examples assume different simplifications:i) they consider input scenarios as local planar scenarios to remove thecomplexity because of geodetics and cartography; ii) the configurationspace is usually well identified from scratch; iii) they assume polygonsdirectly related to the shortest path problem are clustered in limitedareas; iv) they assume small number of simple polygons (defined by a fewvertices).

Some examples do not provide a robust autonomous solution for anygeographic scenario. The examples disclosed herein enable increasedflexibility by providing a robust autonomous solution that addressesdifferent operational scenarios. Some examples include some human tasksto conveniently prepare each operational scenario according to themission requirements. However, the examples disclosed herein includeconsciously preparing the scenarios related to a mission.

The example autonomous definition of the safety offset distanceconsiders the most relevant uncertainty factors. In some examples, theoffset distance is calculated by the sum of two components, a constantcomponent and/or value provided by the user and a second componentand/or value internally calculated by the method. This way, the examplemethod ensures no invasion of the no flight zones and fits better theconfiguration space, making the method more efficient, robust and safe.In contrast, some examples typically work with a constant offset valuethat is initially estimated by users.

The examples disclosed herein increase the automation, efficiency andsafety of unmanned aerial system operations in cases where lateral pathdefinition is used and/or required. In some examples, minimum humanintervention or even no intervention is needed to define pseudo-optimalshortest paths, which is significantly relevant in some situations (e.g.a failure onboard, a critical failure onboard).

The examples disclosed herein reduce the impact on the environment bydetermining and/or selecting the shortest flight path. In some examples,the shortest path is generally associated to the most efficient path interms of fuel consumption. Furthermore, potential risk of incursion innatural protected areas can be reduced if they are included as no flightzones.

To address the issue of the existence of specific performances andlimitations in the unmanned aerial system, in some examples, the examplemethod assumes: i) the turn radius of the unmanned aerial system will beinitially defined and will be constant during the execution of theshortest path (e.g. the worst case turn radius of the unmanned aerialsystem platform may be considered) and; ii) the vertical path of theunmanned aerial system will be constrained to safe and constantaltitudes.

In some examples, safety margins are added to avoid no flight zonesincursions to reduce the high uncertainties associated with the motionpredictability and position accuracy of the unmanned aerial systems.

The examples disclosed herein also reduce the complexity of the scenario(e.g., the initial scenario) by avoiding computation time limitations,to provide the best possible solution into the required time range.

The examples disclosed herein translate the geodetic scenario (e.g., thefirst scenario) into a planar one reducing the complexity of theunmanned aerial system operational scenarios. In some examples, suchtranslations i) distorts planar no flight zones and; ii) increases theuncertainty of the geodetic location of the unmanned aerial system. Toaddress such issues, the examples disclosed herein reduce the distortioninto reasonable values and take them into account in the overallsolution.

Some of the applications or uses of the proposed example methods andsystems may be: advanced unmanned aerial system autonomous contingencymanagement functions such as Return-Home, Lost-Link, Engine-Out andSense & Act capable of avoiding no flight zones in an efficient androbust way and Ground Control Stations (GCS) to support the remote pilotin the modeling of lateral flight paths for unmanned aerial systemoperations. Besides unmanned aerial system applications, the examplemethod may be also valuable in the ATM domain, for trajectory planningand procedure design purposes as well as a baseline algorithm fordynamic trajectory management automation tools such as conflictresolution.

1. A system, comprising: memory storing computer readable code; and atleast one processor to execute the computer readable code to cause theat least one processor to: access an initial scenario including a sourcepoint, a target point, and a no flight zone; determine a computationtime for identifying a lateral path for an aircraft to traverse thatavoids the no flight zone, the computation time being associated with afirst number of vertices of the no flight zone; determine whether thedetermined computation time satisfies a threshold of a referencecomputation time; when the computation time does not satisfy thethreshold of the reference computation time, change the first number ofvertices of the no flight zone to a second number of vertices of the noflight zone to enable a subsequently determined computation time tosatisfy the threshold; determine a buffer area surrounding the no flightzone, wherein the buffer area is defined by an offset distance from aperimeter of the no flight zone; construct a visibility graph includinglateral paths between the source point and the target point, the lateralpaths not passing through the no flight zone, the lateral pathsconnecting the first number of vertices or the second number of verticesof the no flight zone, the first number of vertices or the second numberof vertices taking into account the buffer area; and identify a firstlateral path of the lateral paths, the first lateral path being shorterthan others of the lateral paths.
 2. The system of claim 1, wherein whenthe initial scenario is defined in geodetic coordinates, furtherincluding converting the geodetic coordinates to cartographiccoordinates.
 3. The system of claim 2, wherein converting the geodeticcoordinates to cartographic coordinates includes using a scale factor.4. The system of claim 1, wherein the no flight zone includes a first noflight zone, further including a second no flight zone, and: defining aconfiguration space between the source point and the target point andbounded by a first line intersecting the source point and a second lineintersecting the source point; and identifying the second no flight zoneas being outside of the configuration space.
 5. The system of claim 4,wherein the computation time is a first computation time, in response toidentifying the second no flight zone as being outside of theconfiguration space, determining a second computation time for obtaininga second lateral path that avoids the first no flight zone, thedetermining not considering the second no flight zone.
 6. The system ofclaim 5, wherein the buffer area is a first buffer area, the visibilitygraph is a first visibility graph, and the lateral paths are firstlateral paths, in response to the second computation time satisfying thethreshold of the reference computation time, further including computerreadable code which, when executed, cause the at least one processor to:determine a second buffer area surrounding the first no flight zone;construct a second visibility graph including second lateral pathsbetween the source point and the target point, the second lateral pathsavoiding the first no flight zone; and identify a third lateral path ofthe second lateral paths, the third lateral path being shorter thanothers of the second lateral paths.
 7. The system of claim 6, whereinthe first lateral path is different from the third lateral path.
 8. Thesystem of claim 1, wherein changing the first number of vertices of theno flight zone includes applying a vertex reduction algorithm to the noflight zone.
 9. The system of claim 8, wherein the vertex reductionalgorithm includes at least one of a minimum Bounding Box algorithm or alinear simplification algorithm.
 10. The system of claim 1, wherein thebuffer area includes a first buffer area, further including modifyingthe first buffer area to reduce a size of the first buffer area to asecond buffer area after identifying an angled portion of the firstbuffer area satisfying a threshold.
 11. The system of claim 1, whereinthe no flight zone includes a first no flight zone and a second noflight zone, the first no flight zone overlapping the second no flightzone.
 12. The system of claim 11, further including computer readablecode which, when executed, cause the at least one processor to merge thefirst and second no flight zones when the first no flight zone overlapsthe second no flight zone.
 13. A system, comprising: memory storingcomputer readable code; and at least one processor to execute thecomputer readable code to cause the at least one processor to: define anarea between a source point and a target point; identify a first noflight zone within the area; identify a second no flight zone outside ofthe area; estimate a first computation time to determine a first lateralpath for an aircraft to traverse between the source point and the targetpoint, the estimating to consider the first no flight zone, theestimating not to consider the second no flight zone; compare the firstcomputation time to a reference computation time; modify the first noflight zone to be a third no flight zone when the first computation timedoes not satisfy a threshold of the reference computation time; andestimate a second computation time to determine a second lateral pathfor the aircraft to traverse between the source point and the targetpoint, the estimating to consider the third no flight zone.
 14. Thesystem of claim 13, further including computer readable code which, whenexecuted, cause the at least one processor to define a buffer areaaround the third no flight zone, the estimating to consider the third noflight zone.
 15. The system of claim 14, further including computerreadable code which, when executed, cause the at least one processor toidentify lateral paths between the source point and the target pointwhen the second computation time satisfies the threshold of thereference computation time, the lateral paths not passing through thethird no flight zone, the lateral paths connecting vertices of the thirdno flight zone.
 16. The system of claim 15, further including computerreadable code which, when executed, cause the at least one processor toprocess the lateral paths to identify a third lateral path, the thirdlateral path being shorter than others of the lateral paths.
 17. Thesystem of claim 13, wherein the third no flight zone includes a fourthno flight zone and a fifth no flight zone, the fourth no flight zoneoverlapping the fifth no flight zone.
 18. The system of claim 17,further including computer readable code which, when executed, cause theat least one processor to merge the fourth and fifth no flight zones toform the third no flight zone when the fourth no flight zone overlapsthe fifth no flight zone.
 19. The system of claim 13, wherein modifyingthe first no flight zone to be the third no flight zone includesapplying a vertex reduction algorithm to the first no flight zone.
 20. Asystem, comprising: memory storing computer readable code; and at leastone processor to execute the computer readable code to cause the atleast one processor to: determine an initial path estimate between asource point and a target point associated with a flight of an aircraft;identify a first no flight zone and a second no flight zone; determine afirst buffer area surrounding the first no flight zone and a secondbuffer area surrounding the second no flight zone, wherein the firstbuffer area is defined by an offset distance from a perimeter of thefirst no flight zone and the second buffer area is defined by an offsetdistance from a perimeter of the second no flight zone; identify anoverlap between the first no flight zone including the first buffer areaand the second no flight zone including the second buffer area; mergethe first no flight zone including the first buffer area and the secondno flight zone including the second buffer area into a third no flightzone including a third buffer area when the overlap is identified;construct a visibility graph including lateral paths between the sourcepoint and the target point, the lateral paths not passing through thethird no flight zone including the third buffer area, the lateral pathsconnecting vertices of the third no flight zone; and identify a firstlateral path of the lateral paths, the first lateral path being shorterthan others of the lateral paths.
 21. The system of claim 20, furtherincluding computer readable code which, when executed, cause the atleast one processor to translate the first lateral path to a geodeticpseudo-optimal lateral path for use by the aircraft.
 22. The system ofclaim 20, further including computer readable code which, when executed,cause the at least one processor to cause the aircraft to follow thefirst lateral path.
 23. The system of claim 20, wherein the aircraftincludes an unmanned aerial vehicle.